Non-spherical oscillations of an encapsulated magnetic microbubble

This paper presents a model for non-spherical oscillations of a lipid-encapsulated bubble infused with magnetic particles, developed using membrane theory for thin, weakly magnetic membranes. The model assumes that only the applied magnetic field contributes significantly to the Maxwell stress, with the membrane under generalised plane stress. Axisymmetric deformations are analysed under two external magnetic field configurations: symmetrically arranged current-carrying coils and symmetrically placed magnetic dipoles. The non-spherical oscillations are restricted to the linear regime, with the second mode dominating within the stable pressure range. The pressure–frequency stability region is computed, and its dependence on material properties and magnetic forcing is examined, and natural frequencies are estimated using a boundary-layer approximation. In the coil-field configuration, time-series analysis shows that the second mode attains significant amplitude relative to the bubble radius, increasing with both interfacial magnetic susceptibility and initial radius. Order-of-magnitude estimates indicate that pressure forcing dominates over magnetic forcing, implying a negligible effect of applied current on radial oscillations and stability. In contrast, for the dipole field, increasing dipole strength and reducing its distance from the bubble centre significantly reduces the stability region. Simulations with time-varying current further show that its amplitude and frequency have minimal influence on the stability diagram but strongly affect the periodicity of mode shapes.